# Full text of "Analytical Mechanics"

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WORK
small displacement, the resultant force assumes a value ferent from zero.    If the displacement is small enough that the departure from equilibrium position and coi quently the resultant force remains small, the displacen is called a virtual displacement and the work done by resultant force virtual work.   We will call virtual force small resultant "force, which is called into play by the vir displacement.
Let Fi, Ft, etc., be the forces under the action of wl the particle is in equilibrium. When the particle is giv< virtual displacement ds, these forces are changed, in gem in magnitude and direction so that a virtual force dF , upon the particle during the displacement. Then the vir work is
dF • ds = Fi - dsi + F2 • cfe2 + • • • ,          ("
where dsi, ds%, etc., are the displacements of the par along the forces FI, F2j etc., due to the virtual displaces 'ds. But since the left-hand member of the last equa is an infinitesimal of the second order while the terms oi right-hand member are infinitesimals of the first orde; can neglect the left-hand member and write
Fi ds1+F2ds*> + - •  •   + = 0.               0
Equation (VIII) states: when a particle which is in < librium is given a virtual displacement the total amount of' done by the forces acting upon the particle vanishes. Tl the principle of virtual work.
The principle of virtual work is applicable not onl particles, but also to any system which is in equilibr If the system is acted upon by torques as well as fo then the sum of the work done by the virtual torques the virtual forces vanishes:
• • = 0.